Question

Factor each polynomial x2-36

Answer 1

(x+6)(x-6) would be the factored form

Answer 2

I only see the polynomial $x^2-36$, so I'll factor that one.

We can use two approaches: the most "standard" one requires us to find the roots of the polynomial. Then, for each root $x_i$ we write the factor $(x-x_i)$, and decompose the polynomials like this:

$x^2-36=0 \iff x^2 = 36 \iff x = \pm\sqrt{36} = \pm 6$

So, the root $6$ yields the factor $(x-6)$, and the root $-6$ yields the factor $(x+6)$. This means that the polynomial can be factored as

$x^2-36 = (x+6)(x-6)$

Alternatively, you can observe that the polynomial comes in the form $a^2-b^2$, and it can be factored as

$a^2-b^2 = (a-b)(a+b)$

which again leads to

$x^2-36 = (x)^2 - (6)^2 = (x+6)(x-6)$